This Seeking Tech walkthrough will show you how to beat Mutant Primate without getting hit in Sly 3: Honor Among Thieves (2024) on PS5 and PS4.
Use the following video as a reference:
For the first phase, you will need to run around to dodge your allies when they are thrown at you.
For the second phase, he will be sending minions at you. Focus on shooting the smaller enemies first before attacking the boss.
For the third phase, he will move closer for melee attacks. Jump when he tries to swipe at you and move away from his arms when he tries to slam them down.
Continue attacking him and you should take the boss down without taking damage.